The present invention relates generally to locating frequency agile emitters using RF interferometers, and more specifically, the present invention relates to using a long baseline interferometer (LBI) to make ambiguous and biased signal direction-of-arrival (DOA) phase measurements in a sequence of receiver dwells, possibly all at different signal frequencies, and to locate the emitter by forming phase change estimates by taking differences of the phase measurements between these dwells.
FIG. 1 illustrates the relationship between interferometer baseline, emitter signal angle of arrival, emitter direction of arrival unit vector, and receiver phase measurement fundamental to the understanding of the present invention.
FIG. 1 relates LBI phase measurement to emitter DOA. The LBI baseline 102 is created by antennas 100 and 101. The true phase 104 is the vector dot product of the emitter direction-of-arrival unit vector 106 onto the LBI baseline 102 scaled by the emitter RF carrier frequency f and speed-of-light c, as described by Equation 1:                     φ        =                              f            c                    ⁢                                    d              →                        ·                          u              →                                                          (        1        )            
However, phase measurement 105 is only measured modulo one cycle by the phase detector 107, i.e., as described by Equation 2:                               φ          m                =                              φmod            ⁡                          (                              1                ⁢                                  xe2x80x83                                ⁢                cycle                            )                                =                                                    f                c                            ⁢                                                d                  →                                ·                                  u                  →                                                      -            n                                              (        2        )            
where the integer n is the number of cycles subtracted from the true phase so that the measured phase satisfies the inequality:       -          1      2         less than       φ    m    ≤      1    2  
Determining n to recover the relationship in Equation 1 from Equation 2 is called resolving the phase measurement.
For long baseline interferometers, the inability to robustly and economically calibrate the large cable runs 109 from antennae 100, 101 to receiver means a large unknown bias error 110 is typically present in the LBI phase measurement. But it is well established that accurate emitter range estimation requires only precise measurement of the emitter bearing rate-of-change. See for example, A. L. Haywood xe2x80x9cPassive Ranging by Phase-Rate Techniquesxe2x80x9d (Wright-Patterson AFB Tech. Report ASD-TR-70-46 December 1970). In practice, discrete time phase differences rather than phase rates are used, i.e., as described by Equation 3:                                                         φ              m                        ⁡                          (                              t                2                            )                                -                                    φ              m                        ⁡                          (                              t                1                            )                                      =                                            f              c                        ⁢                                                            d                  →                                2                            ·                                                u                  →                                2                                              -                                    f              c                        ⁢                                                            d                  →                                1                            ·                                                u                  →                                1                                              +                      n            1                    -                      n            2                                              (        3        )            
Here, the phase differences are determined based on measurements typically made one second or more apart.
Using the phase difference, rather than phase, to locate the emitter means the bias errors 110 on the individual measurement from antennae 100, 101 cancel. It also means differential, and not absolute, phase ambiguity resolution of the LBI baseline is required. Kaplan, in xe2x80x9cPassive Ranging Method and Apparatusxe2x80x9d, U.S. Pat. No. 4,734,702, described how to resolve the differential phase measurement ambiguity m=n2xe2x88x92n1 utilizing a short baseline interferometer (SBI). The SBI can be a planar interferometer that measures {right arrow over (u)}sbi. Then, using the procedure outlined in Kaplan, the SBI DOA unit vectors measured at two different points in time, times 1 and 2, are dotted onto the LBI baseline to predict the LBI unambiguous phase and allow m to be found according to Equation 4:                     m        =                                            n              1                        -                          n              2                                =                      nint            ⁡                          (                                                                    φ                    m                                    ⁡                                      (                                          t                      2                                        )                                                  -                                                      φ                    m                                    ⁡                                      (                                          t                      1                                        )                                                  -                                                      f                    c                                    ⁢                                                                                    d                        →                                            2                                        ·                                                                  u                        →                                            sbi2                                                                      +                                                      f                    c                                    ⁢                                                                                    d                        →                                            1                                        ·                                                                  u                        →                                            sbi1                                                                                  )                                                          (        4        )            
where nint is the nearest integer function.
FIG. 2 depicts a realization of the SBI/LBI method using only a linear SBI 200. A linear or one-dimensional interferometer measures AOA (108, FIG. 1) not {right arrow over (u)}sbi (equivalent to 106, FIG. 1). In this case, Equation 4 is utilized in a special sensor-oriented coordinate system, such as the ijk set 103 depicted in FIG. 1. In such sensor coordinates, Equation 4 becomes Equation 5:                                           n            1                    -                      n            2                          =                  nint          ⁡                      (                                                            φ                  m                                ⁡                                  (                                      t                    2                                    )                                            -                                                φ                  m                                ⁡                                  (                                      t                    1                                    )                                            -                                                                    f                    2                                    c                                ⁢                L                ⁢                                  xe2x80x83                                ⁢                                                      cos                    ⁡                                          (                      AOA                      )                                                        sbi2                                            +                                                                    f                    1                                    c                                ⁢                L                ⁢                                  xe2x80x83                                ⁢                                                      cos                    ⁡                                          (                      AOA                      )                                                        sbi1                                                      )                                              (        5        )            
where the obvious modification to handle different frequencies f1 and f2 at each phase measurement has also been incorporated, and L (FIG. 1, 111) is the baseline length. The processing indicated by Equation 5 occurs in process step 202, (FIG. 2). The ambiguity integer is added at step 203 to the measured ambiguous phase determined at step 210, and ambiguous phase change related to emitter range is resolved at step 204, allowing the emitter location to be determined and output, i.e. emitter range and bearing found.
As Equation 1 indicates, to the first order, the resolved LBI phase difference may contain components due to baseline motion and frequency change, as well as phase change due to motion relative to the emitter as described by Equation 6: The component containing emitter-range information, and hence generating the phase change specifically considered by Haywood and Kaplan, is given by the second term, i.e., as described by Equation 7:                               Δφ          range                =                              f            c                    ⁢                                    d              →                        ·            Δ                    ⁢                      xe2x80x83                    ⁢                      u            →                                              (        7        )            
This relation forms the basis for the step 204 processing in conventional SBI/LBI implementations used to locate frequency stable, or non-frequency agile emitters. Against frequency agile emitters, perturbations to the phase due to frequency changes must be accounted for before employing Equation (7).
As shown by the third term in Equation 6, emitter frequency agility alters the xcex94 phase-range relation by introducing a frequency-change and DOA dependent factor. But, as Equation 5 demonstrates, this does not create a problem in SBI/LBI ambiguity resolution if the SBI itself can be resolved. However, SBI design techniques, e.g. as described by Robert L. Goodwin, in xe2x80x9cAmbiguity-Resistant Three and Four-Channel Interferometersxe2x80x9d, (Naval Research Laboratory, Washington, D.C. Report 8005, Sep. 9, 1976), typically assume the same RF carrier frequency for all pulses used to estimate the phase ambiguities and generate COS(AOA). This assumption is almost always valid if the phase across all baselines is measured on the same pulse. Emitter frequency may change intrapulse, e.g. chirped signals, but this is comparatively rare. However, monopulse measurements require a separate receiver pair and phase detector for each SBI baseline. These systems are expensive in terms of both weight and cost and do not exploit the fact that the LBI measurement requires only a single, two channel system, 205 (FIG. 2).
Such a two channel system used with an SBI requires baseline switching, e.g., using an RF switch 201 to connect a single pair of receivers and phase detector 211 sequentially between SBI interferometer antennae 206. Frequency is xe2x80x9csimultaneouslyxe2x80x9d obtained by the instantaneous frequency measurement (IFM) module 207. In this method, the minimum number of pulses collected for a single emitter equals the number of interferometer baselines. But against pulse-to-pulse agile emitters, the IFM measures a different frequency for each pulse. Then, when employing conventional processing, such as described by Goodwin, the SBI ability to resolve phase ambiguities at process step 208 and subsequently use the resolved phase ambiguities to estimate COS(AOA) at step 209 totally fails. Hence, this most desirable two-channel SBI/LBI implementation cannot be used against frequency agile emitters.
Denton, in xe2x80x9cExploitation of Emitter RF Agility for Unambiguous Interferometer Direction Findingxe2x80x9d, U.S. Pat. No. 5,652,590 (hereinafter referred to as the ""590 patent), has demonstrated a way, specific to frequency agile signals, to overcome the above-described two-channel-system drawback by not using an SBI to estimate the COS(AOA). Denton considers the specialization of Equation 1 to sensor coordinates, e.g. ijk, 103 (FIG. 1), as described by Equation 8:                     φ        =                              f            c                    ⁢          L          ⁢                      xe2x80x83                    ⁢                      cos            ⁡                          (              AOA              )                                                          (        8        )            
(with his xcex8=xcfx80/2xe2x88x92AOA) and notes that for emitters with continuously varying frequency, and systems with continuous phase measurements, COS(AOA) can be estimated from the derivative of phase with respect to frequency, i.e., as described by Equation 9:                               cos          ⁡                      (            AOA            )                          =                              c            L                    ⁢                                    ⅆ              φ                                      ⅆ              f                                                          (        9        )            
FIG. 3 indicates how Denton""s technique may be combined with the LBI ambiguity resolution portion of Kaplan""s approach, as depicted in FIG. 2, to perform phase-rate passive ranging against frequency agile emitters. Process esteps 330 and 340, which are embodiments of steps 24 and 25, FIG. 2 of the Denton patent, replace the SBI in Kaplan""s method. The COS(AOA) found via Equation 9 is then used in process step 350 to resolve the LBI between receiver dwells in a manner entirely analogous to the use of the SBI estimate in step 202, (FIG. 2).
Basing COS(AOA) extraction on the relation in Equation 9 assumes the only contributor to phase change in Equation 6 is frequency, that is as described by Equation 10:                     Δφ        =                                            Δ              ⁢                              xe2x80x83                            ⁢              f                        c                    ⁢                                    d              →                        ·                          u              →                                                          (        10        )            
Based on the above, the baseline 102 (FIG. 1) cannot change relative to the DOA unit vector {right arrow over (u)} 106 in a manner causing the relative AOA 108 in Equation 9 to change. Since {right arrow over (u)} is essentially constant over the short time span COS(AOA) is estimated, this means the baseline {right arrow over (d)} must be fixed in space (or restricted to motion on a cone with axial angle AOA about {right arrow over (u)}), i.e. that the term       f    c    ⁢  Δ  ⁢      xe2x80x83    ⁢            d      →        ·          u      →      
in Equation 6 is vanishingly small. As will be seen, this can greatly limit the aircraft""s permissible attitude change, e.g. ability to roll or yaw during the rate estimation process.
Another limitation arises from the fact most agile radars have pulsed signals, thereby rendering continuous time phase and frequency measurements unavailable. Against pulsed signals, the smallest time step possible is one pulse repetition interval (PRI). So, in implementing the method of the ""590 patent, Equation 10 is used to approximate the differentials in Equation 9, where the minimum discrete phase and frequency difference is over a PRI. This assumes the emitter is pulse-to-pulse frequency agile, because Denton requires a different frequency at each discrete phase measurement used to approximate the derivative. If the emitter is batch agile, the differences may span many PRI.
For pulsed signals in particular, the method of the ""590 patent also requires that the phase difference in Equation 10 be unambiguous. Denton states, xe2x80x9cIf two discrete frequencies are measured, the total phase range must be unambiguous, requiring a limit on the baseline length or the frequency range.xe2x80x9d Thus, in applying his technique, the measured phase differences xcex94xcfx86m must satisfy Equation 11a:                               Δφ          m                =                  Δφ          =                                                    Δ                ⁢                                  xe2x80x83                                ⁢                f                            c                        ⁢                                          d                →                            ·                              u                →                                                                        (                  11a                )            
and not Equation 11b:                               Δφ          m                =                              Δφmod            ⁡                          (                              1                ⁢                                  xe2x80x83                                ⁢                cycle                            )                                =                                                                      Δ                  ⁢                                      xe2x80x83                                    ⁢                  f                                c                            ⁢                                                d                  →                                ·                                  u                  →                                                      -            p                                              (                  11b                )            
where p is an ambiguity integer analogous to n1xe2x88x92n2 in Equation 3. Since COS(AOA) is assumed constant in Equation 9, the unambiguous measurement requirement is equivalent to restricting the       od    ⁢          xe2x80x83        ⁢    φ    Ldf
measured values to the interval xc2x11.
Denton notes that, for a signal at 13 dB receiver video signal-to-noise ratio, 600 pulses are required to satisfy his processing error constraints when the maximum frequency change is 100 MHz. FIG. 4 shows the first 100 samples of a typical 600 sample data collection set. In the simulation, the aircraft was flying straight and level with the 10 GHz emitter 90 nautical miles distant at 45xc2x0 relative bearing, and the phase measured on a 40 foot LBI baseline. Spikes 401 and 402 result from jumps in the ambiguity integer p. Measurements with such jumps are readily rejected by restricting the COS(AOA) approximation values to only those in the interval xc2x11, indicated by upper boundary 403. Using the measurements in this region required actually collecting 613 pulses to get 600 usable samples, and from these samples the COS(AOA) was estimated to be 0.0122. This result was in excellent agreement with the true value of 0.0120.
FIG. 5 shows COS(AOA) estimation results for the same scenario, but with aircraft heading variations called xe2x80x9cDutch rollxe2x80x9d added. Dutch roll is a coupled airframe lateral-direction oscillation which is dynamically stable. These small yawing-rolling variations, due to wing dihedral interaction with static airframe directional stability, are largely unavoidable and intrinsic to most aircraft suitable for LEI installations. Dutch roll introduces the phase change component       f    c    ⁢  Δ  ⁢      xe2x80x83    ⁢            d      →        ·          u      →      
which the method of the ""590 patent neglects. Hence, it represents an increase in random measurement noise, described by equation element 112 of FIG. 1, when using Denton""s method. Even though in the simulation the heading change was on the order of 1xc2x0 or less, the long LBI baseline transforms the motion to an appreciable phase error. Now the measurements exceed the acceptance window 503 much more often because the measurement error variance has increased dramatically. Over 700 pulses had to be collected to obtain 600 estimates within the acceptance window. Now, not only cycle skips, indicated by reference numeral 501, but large phase errors, indicated by reference numeral 502, on unambiguous measurements push values outside the constraints of acceptance window 503. The average true COS(AOA) was 0.00667 in this simulation, but the estimated value was xe2x88x920.278. The error in the AOA estimate is about 16.5xc2x0; which generates an error in predicted LBI phase much greater than xc2xd cycle, and is too large to correctly predict phase at step 350, (FIG. 3), on the 40 foot LBI baseline.
Dutch roll represents a relatively benign attitude change with small attitude change rates. Attitude change rates when the aircraft is intentionally maneuvering are much larger. For example, nominal, not extreme, roll rates are on the order of 60xc2x0 per second. Thus, intentional attitude adjustments almost always result in a much greater baseline change than Dutch roll, and correspondingly much larger errors in the COS(AOA) estimate. FIG. 6 shows an example of the degradation in COS(AOA) measurement that occurs with an 8xc2x0 per second yaw during the phase measurement interval. The number of ambiguity cycle skips 600 and large phase noise error 601 created by neglecting f/cxcex94{right arrow over (d)}xc2x7{right arrow over (u)}, both causing the COS(AOA) estimate to fall outside the xc2x11 limit 602, have increased dramatically compared to the no-attitude-change case of FIG. 4. Over 1200 samples were required to get 600 estimates within the acceptance window. But the 600 estimates had such large equivalent phase error created by neglecting the baseline motion that the spatial angle was off by 48.7xc2x0 from the true AOA. Thus, the estimate was useless.
These examples clearly indicate the method of the ""590 patent fails when there are commonly experienced airframe attitude changes unless the induced phase error (601 of FIG. 6, 502 of FIG. 5) can be reduced by either greatly restricting the LBI baseline length or the allowable emitter frequency variations, or greatly extending the data collection interval.
These restrictions greatly limit the usefulness of the method. The main benefit of LBI passive ranging, i.e., rapid convergence to accurate emitter location estimates, depends on having a long LBI length. Also, there is absolutely no control over the emitter frequency behavior: many agile emitters of interest utilize large frequency changes. And extending the data collection requirement from that suggested by Denton is not compatible with other receiver performance requirements.
This is especially true since the 600 pulse requirement alone cannot realistically be supported in most LBI applications, even in the absence of any attitude change. The PRI assumed in the above test was 500 microseconds (xcexcsec), so the 613 pulse data collection took about 0.3 seconds. Some emitter""s have PRI on the order of 5,000 xcexcsec, requiring 3 seconds of data collection. These times represent extremely long receiver dwells on a single emitter. This is disadvantageous as it is generally desirable to reduce the data collection time not only to limit the impact of attitude change on measured phase, but also to improve the receiver""s radar revisit rate and ensure timely detection of new emitters. For all of the above reasons, SBI/LBI pulse collection is usually limited to two pulses per receiver dwell per baseline.
So for an SBI with six antennas, ten pulses are typically collected. It is desirable, at least under the ideal condition of no baseline rotation, to not exceed this number in order to assure all emitters in the environment are detected. But if only the first 10 pulses measured to generate the estimates in FIG. 4 are used in the method of U.S. Pat. No. 5,652,590 to find COS(AOA), the result is xe2x88x920.0492, whereas the true value was 0.0120. Denton""s 600 pulse requirement at 13 dB video SNR definitely cannot be relaxed, even under ideal conditions with the unrealistic assumption of absolutely no baseline attitude change.
In summary, a costly solution to LBI passive ranging against frequency agile emitters involves monopulse direction finding (DF). The method of the ""590 patent provides a potential means to circumvent this costly approach; however, even under the best conditions, the method requires sixty times as many pulses as are conventionally collected to predict LBI phase. Further, even with 600 pulses, the method cannot accurately estimate COS(AOA) in the presence of aircraft attitude changes. Also, the magnitude of the allowable pulse-to-pulse frequency change must be restricted, or the length of the LBI baseline greatly restricted, to guarantee sufficient unambiguous phase difference measurements to perform the required 600 sample statistical processing at 13 dB SNR. Thus, the method described in the ""590 patent is not a robust or practical frequency agile alternative to monopulse SBI for real flight regimes and desirable receiver tuning strategies, or against a significant number of emitters of interest.
These drawbacks stem partly from assuming phase change limited to satisfying Equation (11a) rather than incorporating a more realistic model of short-time phase change which depends also on baseline rotation as described by Equation 12:                     Δφ        =                                            f              c                        ⁢            Δ            ⁢                          xe2x80x83                        ⁢                                          d                →                            ·                              u                →                                              +                                                    Δ                ⁢                                  xe2x80x83                                ⁢                f                            c                        ⁢                                          d                →                            ·                              u                →                                                                        (        12        )            
To handle baseline change according to this model the DOA unit vector must generally be estimated, not just AOA.
The drawbacks also stem from using the rate of phase change with respect to frequency to estimate AOA (24 and 25, FIG. 1 in the ""590 patent). Estimating derivatives from noise-corrupted data requires extensive smoothing, hence the 600 pulse requirement. Also, estimating COS(AOA) from a rate estimate does not provide an efficient way to utilize ambiguous phase differences, i.e. measurements satisfying Equation (11b). As a result, restrictions must be placed on the xe2x80x9cfrequency-change times baselinexe2x80x9d product to ensure most measurements are unambiguous, and further hope that the RF signal is uniformly distributed over its agile bandwidth, or has another distribution guaranteeing a significant number of small frequency changes. But, even for a uniform frequency distribution, ambiguous measurements can make up most of the phase-difference estimates for a large class of agile emitters when only 10 pulse phase measurements are taken, as the results shown in FIG. 4 demonstrate. And because radars use frequency agility either as an electronic counter countermeasure (ECCM), or to enhance performance, there is no necessary reason for them to use a uniform frequency distribution. For example, an ECCM application is frequency hopping within a bandwidth, possibly extending over 1 GHz (compared to the 100 MHz bandwidth considered in the above examples), to reduce the vulnerability of surface-to-air missile systems to jamming. In doing this, the radar designer may place a limit on the minimum allowable frequency change. Such a radar may provide very few unambiguous phase differences on a 40 foot LBI baseline, even when 600 pulses are sampled.
The present invention overcomes these drawbacks and deficiencies by exploiting emitter frequency agility to estimate both COS(AOA) and {right arrow over (u)}, but does not use estimates of the rate of phase change with respect to frequency. The method requires only three frequency-phase measurements in high SNR conditions, and ten at 13 dB under ideal conditions. Although it can use an unlimited number of measurements, and places no intrinsic restriction on aircraft attitude change during the pulse collection process, the most required under the worst conditions studied is 60 measurements. Rapid attitude change may, in fact, generate more accurate angle estimates from fewer measurements than straight and level flight. Also, the new method places no restriction on the maximum allowable frequency change. Large frequency changes actually enhance the method performance and each measured phase difference can be ambiguous.